Method and apparatus for locating and aligning golf club shaft spine

ABSTRACT

The preferred orientation, or planar oscillation plane, of a golf club shaft is located by measuring the oscillation of the shaft when a horizontal impulse is applied and from those measurements determining an orientation in which the oscillation would be substantially planar. In a preferred embodiment an iterative process is used to converge on the preferred orientation. The location of the preferred orientation may be marked on the shaft and used to assemble a golf club with the planar oscillation plane in a predetermined orientation. The assembly of the golf club can be done manually—e.g., in a refitting situation—or automatically—e.g., in a new club manufacturing setting.

CROSS REFERENCE TO RELATED APPLICATION

[0001] This claims the benefit of copending United States ProvisionalPatent Application No. 60/135,012, filed May 20, 1999.

BACKGROUND OF THE INVENTION

[0002] This invention relates to locating and aligning the spine of agolf club shaft. More particularly, this invention relates to a methodand apparatus for automatically and reliably identifying the location ofthe spine of a golf club shaft and for aligning the spine in a desiredorientation.

[0003] When a golfer swings a golf club, the shaft of the golf clubbends or twists, especially during the downswing. The direction theshaft bends or twists is dependent on how the golfer loads oraccelerates the club, but the bending or twisting direction andmagnitude also are dependent on the stiffness of the shaft. If a shaftis soft, it will bend or twist more during a given downswing than if itis stiff. Additionally if a shaft exhibits different transversestiffness in different planes—i.e., the stiffness, roundness andstraightness of the shaft are not symmetric—the shaft will bend or twistdifferently depending upon in which plane (direction) it is loaded.

[0004] Immediately prior to the impact of the head of a golf club with agolf ball, the shaft of the golf club goes through significant vibratorymovements in both the toe up/down direction (plane perpendicular to thehit direction) and in the lead/lag direction (plane parallel to the hitdirection). Research has shown the shaft of a golf club vibrates up anddown in the toe up/down direction immediately prior to impact with thegolf ball. This up and down movement, known as “vertical deflection” or“droop,” can be as large as ±1.5 inch (±3.8 cm). Because anyinconsistent bending or twisting due to asymmetric shaft behaviorimmediately prior to impact is substantially impossible for the golferto correct with his or her swing, any reduction in vertical deflectionor droop immediately prior to impact will help the golfer improve his orher impact repeatability. This is true for golfers of all skill levels.Inconsistent bending or twisting makes it more difficult for the golferto reproduce the downswing shaft bending or twisting from club to club,thereby resulting in less consistent impact repeatability within theset.

[0005] In addition, a golf club, immediately prior to impact, “springs”forward in the direction of the shot. This is commonly referred to asthe “kick” of the shaft. If it is possible to analyze and orient a shaftin a way so that the kick direction of vibration is stable, this shaftposition would improve the golfer's ability to repeat the impactposition with the ball. In other words the shaft would have less of atendency to “bob” up and down immediately prior to impact therebyimproving impact repeatability.

[0006] Inconsistent bending or twisting contributes to movements of theclub head that would not be present if the shaft had been perfectlysymmetric. Golf club shaft manufacturers attempt to build shafts withsymmetric stiffness to minimize inconsistent bending or twisting duringthe swing, but as a result of manufacturing limitations it is difficultto build a perfectly symmetric golf club shaft. Specifically, it is wellknown that, as a result of irregularities or variations in materials ormanufacturing processes, golf club shafts have a preferred angularorientation or “spine.” (See, e.g., U.S. Pat. Nos. 4,958,834 and5,040,279, which are hereby incorporated by reference in theirentireties.) Therefore, substantially all golf club shafts exhibit somedegree of asymmetry which results in some degree of inconsistent bendingor twisting during the swing.

[0007] The asymmetric stiffness of golf club shafts can result fromnonsymmetrical cross sections (shafts whose cross sections are not roundor whose wall thickness is not uniform), shafts that are not straight,or shafts whose material properties vary around the circumference of theshaft cross section. Because it is substantially impossible to build aperfectly symmetric golf club shaft and the objective is to minimizeinconsistencies from club to club in a golf club set and from set to setwithin a brand, it makes sense, if possible, to analyze each golf clubshaft in a set of golf clubs to understand its asymmetric bending ortwisting behavior and construct the golf clubs in the set to maximizeconsistency from club to club within a set and from set to set within abrand.

[0008] It has been recognized—e.g., in above-incorporated U.S. Pat. No.5,040,279—that although substantially all golf club shafts exhibit somedegree of asymmetry, substantially every golf club shaft exhibits atleast one orientation in which, when the shaft is clamped at itsproximal, or handle, end and displaced at the tip, the resultantvibration of the shaft will remain substantially planar. That is, theshaft will remain substantially in a single plane and the tip of theshaft will vibrate back and forth substantially along a line.

[0009] It is also recognized in above-incorporated U.S. Pat. No.4,958,834 that the construction of all golf clubs within a set withtheir respective planar oscillation planes (“POPs”) oriented in the sameangular direction relative to their respective club faces will exhibitless inconsistency in shaft bending or twisting during the downswingthan a set that has been haphazardly or randomly constructed. Inparticular, a set of golf clubs normally will function best if therespective preferred angular orientations of the respective golf clubshafts are aligned in the “hit direction”—i.e., substantiallyperpendicularly to the respective golf club faces.

[0010] However, heretofore there has not been any convenient automatedway to determine the preferred angular orientation of a golf club shaft.It would be desirable to be able to provide a method and apparatus forquickly and reliably determining the preferred angular orientation of agolf club shaft. It also would be desirable to be able to provide amethod and apparatus for using the determination of the preferredangular orientation to automatically assemble golf clubs with eachrespective golf club shaft consistently aligned relative to therespective club face.

SUMMARY OF THE INVENTION

[0011] It is an object of this invention to attempt to provide a methodand apparatus for quickly and reliably determining the preferred angularorientation of a golf club shaft.

[0012] It is also an object of this invention to attempt to provide amethod and apparatus for using the determination of the preferredangular orientation—e.g., the planar oscillation plane—to automaticallyassemble golf clubs with each respective golf club shaft consistentlyaligned relative to the respective club face.

[0013] In accordance with the present invention, there is provided amethod of determining a preferred angular orientation of a golf clubshaft about a longitudinal axis thereof, where the golf club shaft has aproximal end for gripping by a golfer and a distal end for attachment toa golf club head. According to the method, the proximal end of said golfclub shaft is immobilized, and vibratory motion of the distal end of thegolf club shaft is initiated in a direction other than parallel to thelongitudinal axis. The vibratory motion is analyzed, and from theanalyzed vibratory motion -he preferred angular orientation iscalculated. The golf club shaft can then be marked to indicate thepreferred angular orientation. In a further method according to theinvention, the mark on the shaft indicating the preferred angularorientation can be used to automatically assemble a golf club with thegolf club shaft in a predetermined alignment relative to the face of thegolf club head.

[0014] Apparatus for determining the preferred angular orientation, andfor assembling golf clubs, are also provided.

BRIEF DESCRIPTION OF THE DRAWINGS

[0015] The above and other objects and advantages of the invention willbe apparent upon consideration of the following detailed description,taken in conjunction with the accompanying drawings, in which likereference characters refer to like parts throughout, and in which:

[0016]FIG. 1 is a diagram in which a flexible golf shaft is modeled as ashaft to which springs are attached;

[0017]FIG. 2 shows the horizontal and vertical displacement, seenend-on, of the shaft of FIG. 1 as a function of time, over twooscillation cycles after an impulse is delivered to cause the shaft tooscillate;

[0018]FIG. 3 shows the motion diagramed in FIG. 2 as a phase plot;

[0019]FIG. 4 shows the motion of the shaft as a phase plot, afterfourteen oscillation cycles;

[0020]FIG. 5 shows the motion diagramed in FIG. 4, but as a function oftime;

[0021]FIG. 6 is a perspective view of apparatus according to the presentinvention for determining the preferred orientation of a golf clubshaft;

[0022]FIG. 7 is a perspective view of a shaft testing assembly of theapparatus of FIG. 6;

[0023]FIG. 8 is a perspective view of a shaft holding and rotatingassembly of the apparatus of FIGS. 6 and 7;

[0024]FIG. 9 is a perspective view of a measurement assembly of theapparatus of FIGS. 6-8;

[0025]FIG. 10 is a perspective view of a tip mass and sensor assembly ofthe apparatus of FIGS. 6-9;

[0026]FIG. 11 is a view similar to FIG. 7 with a golf club shaft mountedin the apparatus;

[0027]FIG. 12 is an end elevational view, taken from line 12-12 of FIG.11, but with the golf club shaft deflected in preparation foroscillation according to the invention;

[0028]FIG. 13 is perspective view of the apparatus of FIGS. 6-10 with amarking assembly included;

[0029]FIG. 14 is a flow diagram of a preferred embodiment of a methodaccording to the invention for location the preferred orientation of agolf club shaft;

[0030]FIG. 15 is a flow diagram of a load test performed according tothe invention as part of the method of FIG. 14;

[0031]FIG. 16 is a flow diagram of a “logo up” comparison test performedaccording to the invention as part of the method of FIG. 14;

[0032]FIG. 17 is a flow diagram of a planar oscillation plane locatingtest performed according to the invention as part of the method of FIG.14;

[0033]FIG. 18 is a diagrammatic view of apparatus according to theinvention for assembling golf clubs; and

[0034]FIG. 19 is a close-up view of an assembly station of the apparatusof FIG. 18.

DETAILED DESCRIPTION OF THE INVENTION

[0035] If a golf club shaft is immobilized at its handle end anddisplaced in a direction perpendicular to its longitudinal axis, then ifthe displacement direction lies in the planar oscillation plane of theshaft, the shaft will vibrate in that plane and, viewed end on, thedistal tip of the shaft will oscillate back and forth along a line. Forconvenience, that line can be referred to as the x-axis. However, if thedisplacement direction is in a plane other than the planar oscillationplane, the distal tip of the shaft will vibrate in a motion havingcomponents along the x-axis as well as along an axis perpendicular tothe x-axis, which for convenience can be referred to as the y-axis. Thismotion could be described as an “orbital” motion, although rather thantracing a single ellipse or other closed curve, the tip will move withinan envelope such that, if the motion would not damp out (as it inreality does), the tip eventually would move through every point withinthat envelope.

[0036] As described below, by observing the tip vibration of the shaft,one can calculate mathematically the orientation of the planaroscillation plane or planes. Having located the planar oscillationplane, one can then assemble a golf club, orienting the shaft relativeto the golf club head so that the planar oscillation plane is lined upalong the “hit direction”—i.e., substantially perpendicular to thehitting face of the club head. It is also possible, having located theplanar oscillation plane of a golf club shaft, to align the planaroscillation plane relative to the golf club head not along the hitdirection, but in another predetermined direction. For example, it maybe desirable to align the shaft for a particular golfer to correct orinduce a hook or a slice.

[0037] It has been observed empirically that a golf club shaft isstiffer in one direction along any planar oscillation plane than it isin the opposite direction along that planar oscillation plane. Thiscorresponds to a stiffer side of the planar oscillation plane of theshaft, which can be referred to as the “hard” or “forward” side of theplanar oscillation plane, while the less stiff side, 180° opposite thehard side, can be referred to as the “soft” or “rear” side of the planaroscillation plane. It has further been observed that while orienting theplanar oscillation plane perpendicular to the club head face brings aclear and dramatic improvement over a haphazard or random alignment,aligning the planar oscillation plane perpendicular to the club headface with the hard side of the planar oscillation plane facing towardthe club head face brings an even further improvement, as compared toaligning the planar oscillation plane perpendicular to the club headface with the soft side of the planar oscillation plane facing towardthe club head face. Moreover, if every golf club in a set of golf clubsis similarly aligned, there is a greater likelihood that the user ofthose clubs will be able to achieve more uniform and consistent resultsacross all golf clubs in the set, which can be expected to result inperformance enhancement.

[0038] In addition, it has been observed empirically that a golf clubshaft may have several planar oscillation planes. However, it has beenfound that there is a principal planar oscillation plane (“PPOP”), whichalso may be referred to as the plane of uniform repeatability (“PURE”),that corresponds to the “spine” of the golf club shaft. Golf clubsaligned based on the principal planar oscillation plane can be expectedto result in optimal performance enhancement.

[0039] The preferred direction of the planar oscillation plane—i.e., inthe case of the principal planar oscillation plane, the “hard” side ofthe spine of the golf club shaft—cannot be determined mathematicallyfrom mere observation of the shaft tip. Therefore, in a preferredembodiment of the invention, the handle end of the golf club shaft isimmobilized, the tip of the shaft is displaced perpendicular to thelongitudinal axis, and the restoring force—i.e., the force tending tomove the tip back to its neutral position—is measured while the shaft isrotated, from the handle end, through at least about 360°. The angle atwhich the restoring force is greatest is an indication of the hard sideof the spine of the shaft. Although this angle usually will not alignprecisely with the orientation of the principal planar oscillationplane, it will indicate which of the two possible orientations of theprincipal planar oscillation plane corresponds to the hard side of theprincipal planar oscillation plane. Moreover, starting one's analysis atthe angle of maximum load can be expected to lead one to find theprincipal planar oscillation plane rather than one of the other planaroscillation planes of the shaft.

[0040] Although it is possible to derive the orientation of the planaroscillation plane precisely using mathematical techniques based on datacollected by displacing the shaft tip and allowing the shaft to vibrate,it is computationally simpler to derive the orientation by an iterativetechnique as described below. In such a technique, the startingorientation can be selected arbitrarily, but preferably the startingorientation is the angle of maximum restoring force, determined asdescribed above, to maximize the likelihood that the planar oscillationplane that is found is the principal planar oscillation plane.

[0041] Once the preferred angular orientation of the golf club shaft hasbeen determined, a mark preferably is made on the shaft to indicate thepreferred angular orientation. The mark may be made at the location ofthe planar oscillation plane, or at a predetermined relative positionwith respect to the planar oscillation plane. This mark can be madeusing ink or paint, or can be etched into the surface of the shaft usingmechanical, electrostatic or laser marking techniques. Once the mark hasbeen made, it can be used to align the shaft relative to a golf clubhead when assembling a golf club, so that the spine of the golf clubshaft is substantially perpendicular to, or at some other desiredorientation with respect to, the club head face.

[0042] The alignment of the shaft to the club head can be performedmanually. Preferably, alignment is facilitated by providing a marking onthe club head as well, near the hosel, to which the marking on the shaftcan be aligned to form a properly “spine-aligned” golf club.Alternatively, in another preferred embodiment, an assembly machinemates a golf club head to a golf club shaft, matching up the alignmentmarkings in the process. In this embodiment, the golf club head can beattached to the shaft immediately after determination of the preferredangular orientation of the shaft, with the shaft still in the chuck ofthe spine locating station (in that case, the application of a visiblemark to the shaft exterior can be omitted, although it would still beuseful for later repair operations when the club is disassembled).Alternatively, in a second variant of this embodiment, the shaft can beremoved from the spine locating station and moved to a club assemblystation. This variant better accounts for any speed differential betweenthe spine locating process and the club assembly process. If the spinelocating process is faster than the club assembly process, more clubassembly stations than spine locating stations can be provided. If theclub assembly process is faster than the spine locating process, morespine locating stations than club assembly stations can be provided. Ineither case, it is preferable to provide a hopper or other intermediatestation for holding spine-aligned shafts between the spine locatingstation and the club assembly station. Normally, one would expect fewshafts to be held in the hopper, but if for some reason there is abreakdown or other bottleneck at or downstream of the club assemblystation or stations, the hopper can serve, until it is full, as areservoir to accept shafts from the spine locating station or stations.

[0043] The invention will now be described with reference to FIGS. 1-19.

[0044] If the handle end of a golf club shaft is clamped in clamp thatholds the shaft horizontally, then looking toward the tip of the distalend of the shaft, the shaft stiffness can be modeled, as shown inFIG. 1. As seen in FIG. 1, shaft 10 can be considered as a mass m havingtwo springs of different spring constants k₁ and k₂ connecting it in twoorthogonal directions to two different surfaces 11, 12. If shaft 10 weresymmetrically stiff, then k₁ and k₂ would be equal. Normally, however,k₁ and k₂ are different. In fact, if one were to clamp the shaft inseveral different orientations, and each time measure the horizontal andvertical restoring forces, one might get different sets of values for k₁and k₂. The force F, as shown, is the force imposed to displace the tipof clamped shaft 10, e.g., to cause the tip to oscillate. ordinarily,the values of k₁ and k₂ are within about 5% of one another. FIG. 2 showsthe normalized horizontal and vertical displacement of the vibrating tipof shaft 10 as a function of time over two oscillation cycles, withhorizontal displacement (x) represented by the solid line 20 andvertical displacement (y) represented by the broken line 21, assumingthe initial displacing force is imposed at an angle θ=40° to thehorizontal. FIG. 3 shows the same displacement of the tip of shaft 10 asa phase plot 30, over two cycles, in x and y—i.e., FIG. 3 shows twocycles of the path the tip follows as it would be seen by an observerviewing the tip along the longitudinal axis of shaft 10, looking towardthe handle end. FIG. 4 shows the phase plot 40 after fourteen cycles.Analysis of these observed motions yields the location of the planaroscillation plane—i.e., the angular orientation of shaft 10 in which, ifthe initial displacing force F were applied along that orientation,shaft 10 would oscillate substantially only along that orientation, withthe tip tracing back and forth substantially along a line.

[0045] As seen in FIG. 4, the phase plot 40 of the tip motion after asufficient number of cycles is substantially a rectangle. Theorientation of the planar oscillation plane is that of one of the twoorthogonal axes of that rectangle, where each axis of a rectangle isdefined as a line midway between, and parallel to, a respective pair ofsides of the rectangle. In the case of a true rectangle, it would besufficient to determine the orientations of the sides, as theorientations of the sides and the axes, according to the definition justset forth, are identical. However, the phase plot 40 of the tip motionof a golf shaft may not be a true rectangle, unless one observes aninfinite number of cycles, which is impractical because, first, it wouldnot be commercially acceptable and, second, the oscillations of the golfclub shaft ordinarily damp out before a true rectangle could beobserved. Therefore, the orientation of each of the two axes may becalculated by assuming that lines drawn through the four vertices of thequasi-rectangular shape of the phase plot are the diagonals of therectangle.

[0046] Having found the two axes of the rectangle, it is desirable todetermine which one is the major axis, which may correspond to theprincipal planar oscillation plane, and which is a minor axis—i.e., oneof one or more unstable planar oscillation planes. This can bedetermined rigorously by measuring the oscillation frequencies alongthose two axes, as described below. The major axis would be expected tocorrespond to the principal planar oscillation plane if the shaft wascaused to vibrate along a direction determined by measuring the load onthe deflected shaft as function of angle, and choosing the angle ofmaximum load as the direction in which to vibrate the shaft. It shouldbe noted that this “load test” could be carried out by clamping eitherthe tip or distal end, or the handle or proximal end, of the shaft, andmeasuring the load as a function of angle with the unclamped enddeflected. In addition, the subsequent steps of locating the planaroscillation plane can be carried out with either end clamped and theunclamped end deflected. However, the subsequent steps of locating theplanar oscillation plane preferably are carried out with the handle orproximal end clamped, and therefore the load test preferably is carriedout that way as well. It should also be noted that if the load test isnot carried out, one may find a planar oscillation plane, but thatplanar oscillation plane likely will not be the principal planaroscillation plane.

[0047]FIG. 5 shows a plot 50 of tip oscillation as a function of time,with a separate trace 51 for oscillations measured along the horizontal(x) axis and a separate trace 52 for oscillations measured along thevertical (y) axis. From these traces, frequency can be determined—e.g.,graphically by counting the positive-going zero crossings. However,these horizontal and vertical axes x and y are offset from the planaroscillation plane by an angle determined as described above. If thatangle is denoted θ, then the frequencies along these axes x and y asdetermined from the plot in FIG. 5 can be transformed into thecoordinate system of the golf club shaft, having axes x′ and y′ thatcorrespond to a stable planar oscillation plane and one of one or moreunstable planar oscillation planes, as follows, where f₁ is thefrequency at an angle θ from the x-axis—i.e., along the x′-axis, and f₂is the frequency at an angle θ from the y-axis (θ+90° from thex-axis)—i.e., along the y′-axis:$f_{1} = {\frac{f_{x}{f_{y}\left( {{{- f_{y}^{2}}\cos^{2}\theta} + {2f_{y}^{2}\cos^{4}\theta} - {3f_{x}^{2}\cos^{2}\theta} + {2f_{x}^{2}\cos^{4}\theta}} \right)}^{0.5}}{{f_{y}^{2}\cos^{2}\theta} + {f_{x}^{2}\cos^{2}\theta} - f_{x}^{2}}}$$f_{2} = {\frac{f_{x}{f_{y}\left( {f_{y}^{2} - {3f_{y}^{2}\cos^{2}\theta} + {2f_{y}^{2}\cos^{4}\theta} - {f_{x}^{2}\cos^{2}\theta} + {2f_{x}^{2}\cos^{4}\theta}} \right)}^{0.5}}{{f_{y}^{2}\cos^{2}\theta} + {f_{x}^{2}\cos^{2}\theta} - f_{x}^{2}}}$

[0048] If f₁ is greater than f₂, then one of the stable planaroscillation planes of the golf club shaft is at an angle θ with respectto the x-axis. If f₁ is less than f₂, then one of the stable planaroscillation planes of the golf club shaft is at an angle θ with respectto the y-axis—i.e., θ+90° with respect to the x-axis. If the load testhas been performed and used to determine the initial angle of vibration,than the stable planar oscillation plane so located can be expected tobe the principal planar oscillation plane.

[0049] Although this mathematical technique, for determining which ofthe planar oscillation planes already identified is the principal planaroscillation plane, is rigorous and precise, it is more computationallyintensive than is necessary in view of the objective. Therefore, inanother preferred embodiment of the invention, as described above and inmore detail below, the location of the principal planar oscillationplane is located to a first-order approximation—i.e., at least to withinthe correct quadrant—by determining the orientation of the direction ofgreatest resistance to bending or twisting of the golf club shaft. Thishas the further benefit of quickly identifying the “forward” directionof the principal planar oscillation plane, as described above.

[0050] A preferred embodiment of apparatus 60 for implementing thepresent invention is shown in FIGS. 6-13. Although apparatus 60 could bemade to implement the rigorous mathematics set forth above, it has beendetermined in practice that a simpler iterative process as describedbelow achieves acceptable results at lower cost. Therefore, in aparticularly preferred embodiment, apparatus 60 uses that simplerprocess.

[0051] In the preferred embodiment, apparatus 60 includes shaft testingassembly 70 and processing unit 61. Processing unit 61 can be any systemcapable of processing input data from sensors 73 and 74 of shaft testingassembly 70 and performing either the rigorous mathematical calculationsdescribed above or the simpler iterative calculations described below.As shown in FIG. 6, processor 61 is preferably a general purposecomputer such as a personal computer, which may, e.g., be based on aPENTIUM® central processing unit (CPU) 62 available from IntelCorporation, of Santa Clara, Calif., running a version of the WINDOWS®operating system available from Microsoft Corporation, of Redmond,Wash., and programmed with software as described below. However,processor 61 could also be hard-wired circuitry or one or moreprogrammed programmable logic devices dedicated to the functionsnecessary to locate the spine of a golf club shaft. In any event,processor 61 preferably also includes memory 63 and mass storage 64.

[0052] Shaft testing assembly 70 preferably includes an elongated base71, which is at least as long a golf club shaft. At one end of base 71is a measurement assembly 72, including a deflector assembly 73 and adeflection load sensor 74. At the other end of base 71 is a shaftholding and rotating assembly 75, including a rotatable chuck 76 forholding a golf club shaft. Apparatus 60 also includes a tip mass andsensor assembly 77 which during testing of a golf club shaft is mountedon the distal end of the golf club shaft and cooperates with deflectorassembly 73.

[0053] As seen in FIG. 8, shaft holding and rotating assembly 75preferably includes rotatable chuck 76 which preferably may beconventional, preferably holding a golf club shaft by exerting radiallyinward force substantially evenly around the shaft circumference. Chuck76 preferably is mounted at the end of axle 80, which preferably isjournalled in bearings 81. Bearings 81 preferably are mounted onsupports 82 so that the axis of rotation of axle 80, and by extensionthat of chuck 76 and the golf club shaft being tested, is at apredetermined height above base 71. The end of axle 80 remote from chuck76 preferably is connected via universal joint 83 to a potentiometer 84that is used as an angular position sensor as described below. Universaljoint 83 prevents any slight misalignment between the axis of axle 80and the shaft of potentiometer 84 from damaging potentiometer 84.Similarly, a traveling nut 85 preferably is provided on axle 80 to actas a rotational stop to limit rotation of axle 80 and thereby preventdamage that might result from overrotation of potentiometer 84. Anoptional motor 86 may be provided to rotate chuck 76, although manualrotation can also be used. In addition it is preferably to provide aclamp 87 to minimize vibrations of chuck 76 as it rotates. Clamp 87preferably provides a friction fit to chuck 76 that is just light enoughto allow rotation of chuck 76. Screws 88 may be provided to adjust thejaw of clamp 87.

[0054] As seen in FIG. 9, measurement assembly 72 includes a base plate90 that is mounted to base 71. A load cell 91, such as a Model LCAE-2KG,available from Omega Engineering, Inc., of Stamford, Conn., is mountedto base plate 90, and a shaft tip restraining arm 92 is mounted to loadcell 91 on the side of load cell 91 opposite base plate 90, for apurpose to be described below. Measurement assembly 72 also preferablyincludes a deflector arm 93 pivotably mounted to base plate 90.Preferably, deflector arm 93 is mounted so that at least one side 930thereof is substantially perpendicular to base plate 90, and so that itpivots about an axis 94 that is substantially parallel to base plate 90.

[0055] Deflector arm 93 preferably has a projection 931, preferablyextending from side 930 thereof. Projection 931 preferably has a surface932 facing away from axis 94 that bears substantially the same angularrelationship to side 930 as does side 100 of tip mass and sensorassembly 77 to side 101 of tip mass and sensor assembly 77, for reasonsdescribed below.

[0056] As shown in FIG. 10, tip mass and sensor assembly 77 preferablyhas a body 102 with a mass of between about 190 grams and about 220grams, and preferably about 200 grams, to simulate the mass of a golfclub head at the distal end of a golf club shaft. In another embodiment,different tip masses could be provided to more closely simulatedifferent types of club heads, which have different masses. However,this latter embodiment would be more costly, insofar as each differentmass would need its own set of transducers to collect displacement data,as well as different computations based on those data.

[0057] The presence of body 102 on the end of a golf club shaft when theshaft is deflected and allowed to oscillate during testing in accordancewith the present invention, as described below, not only mimics theeffect of a club head during a swing, but also provides “reaction mass”that prevents the shaft oscillations from damping out before sufficientdata can be collected. The transducers that collect the displacementdata preferably are two accelerometers 103, 104—such as Model 8303Aavailable from Kistler Instrument Corp. of Amherst, N.Y.—aligned alongtwo different axes. Preferably, the two axes are orthogonal to oneanother, but that is not necessary; as long as the angular relationshipbetween the axes is known, the motion recorded by accelerometers 103,104 can be resolved computationally into two orthogonal components. Alsopreferably, the two axes are parallel and perpendicular, respectively,to base 71. Again, however, that is not necessary.

[0058] Tip mass and sensor assembly 77 preferably has an attachmentstructure for attaching to the tip of a golf club shaft. Preferably, theattachment structure includes a bore 105, slightly larger in diameterthan an average golf club shaft, in body 102, into which the shaft maybe introduced, and a set screw 106 for tightening body 102 onto theshaft. Alternatively, some sort of quick-release clamp can be provided,particularly for use in an automated system as described below.

[0059] As discussed above, there preferably is the same relationshipbetween the orientations of sides 100, 101 of tip mass and sensorassembly 77 as there is between surfaces 930, 932 of deflector arm 93.This is so that tip mass and sensor assembly 77 can be repeatedly linedup the same way for every test, by resting sides 100, 101 againstsurfaces 930, 932.

[0060] In order to test a golf club shaft, the shaft 110 is mounted inchuck 76 as shown in FIG. 11. The tip, or distal end, of shaft 110 isthen deflected and restrained under the lip 120 of shaft tip restrainingarm 92, as shown in phantom in FIG. 11, so that the restoring forcetending to straighten shaft 110 can be measured by load cell 91. Chuck76 is then rotated—manually, or by motor 86 preferably under control ofprocessor 61—while the restoring force is recorded by computer 61 as afunction of angle, which is determined by potentiometer 84, to which aknown voltage is applied. By well-known voltage divider techniques, thechanging resistance is translated to a changing voltage, which can beconverted to an angle.

[0061] It might be expected that when the upward restoring force is amaximum, then the point of maximum asymmetry of the shaft, representingthe hard side of the principal planar oscillation plane, is facingupward. It has been found empirically, however, that that is not so, butthat the hard side is within the quadrant that is facing upward when themaximum force is measured. The angle of the maximum force is thereforerecorded in this static portion of the test, and the remainder of thetest, which is dynamic, is conducted.

[0062] In the dynamic portion of the test, the tip or distal end of golfshaft 110 is oscillated with tip mass and sensor assembly 77 in place.While in the static portion of the test the tip preferably is deflectedvertically, in the dynamic portion of the test the deflection ispreferably horizontal, although any direction can be used in eitherportion of the test. The reason for preferring horizontal deflection inthe dynamic portion of the test is that, first, the effect, on theresults, of gravity acting on the tip mass is minimized, and, second, itis easier to oscillate the shaft without it hitting base 71. Therefore,before the dynamic portion of the test is initiated, chuck 76 preferablyis rotated about 900, so that the estimated orientation of the spine, orprincipal planar oscillation plane, which had been vertical, is nowhorizontal.

[0063] In the apparatus so far described, tip mass and sensor assembly77 is applied, and a horizontal impulse is imparted, to golf club shaft110, as follows. With the proximal or handle end 111 of golf club shaft110 held in chuck 76, and deflector arm 93 standing erect, bore 105 inbody 102 of tip mass and sensor assembly 77 is placed over distal or tipend 112 of golf club shaft 110. Tip mass and sensor assembly 77 is thenmanipulated until surfaces 100, 101 of body 102 are firmly seatedagainst surfaces 930, 932 of deflector arm 93, placing accelerometers103, 104 in their predetermined desired orientations. A portion ofsurface 100 not occupied by accelerometer 103 is used for this purpose,so that accelerometer 103 does not interfere with the seating of body102. Although accelerometers 103, 104 are shown connected to processor61 by wires 62, a wireless connection (not shown) could be provided.

[0064] A preferably substantially horizontal impulse is provided to tipmass and sensor assembly 77 by deflecting tip 112 of golf club shaft 110to side 120 of deflector arm 93 opposite side 930, as seen in FIG. 12,and then, preferably in a sudden motion, pivoting deflector arm 93 outof its erect position, allowing the restoring force in deflected golfclub shaft 110 to provide a horizontal impulse to start tip 112 of golfclub shaft 110 to begin vibrating, along with tip mass and sensorassembly 77, in the manner described above in connection with FIGS. 2-5.

[0065] Although the initial deflection of golf club shaft 110 behinddeflector arm 93, as well as the pivoting of deflector arm 93 to allowtip 112 to oscillate, can be accomplished manually, they can also beaccomplished automatically. Thus, an arm 121 bearing a finger 122,driven by a motor 123 through suitable gearing or linkage 124 thatprovides the necessary horizontal and vertical components of motion, canbe used to move tip 112 of golf club shaft 110 from its neutral position1200 to the position behind deflector arm 93. This could involve bothvertical and horizontal movement of tip 110 by finger 122, or finger 122could move solely horizontally while motor 125 pivots deflector arm 93out of the way temporarily and then restores deflector arm 93 to theerect position. Similarly, the pivoting of deflector arm 93 to allowoscillation to begin can be performed by motor 125 instead of manually.

[0066] As a further alternative, instead of applying an impulse bydeflecting shaft 110 behind deflector arm 93 and then releasing arm 93,a horizontal plunger or ram (not shown) could be used to strike tip massand sensor assembly 77 rapidly and for a short time.

[0067] Each of accelerometers 103, 104 records acceleration in one oftwo respective directions, which preferably are orthogonal to oneanother, and preferably are horizontal and vertical, respectively.However, any two directions may be used, as long as they are known, andthe horizontal and vertical components can be calculated. Theaccelerations preferably are integrated over time to determinehorizontal and vertical displacements. Alternatively, displacement canbe measured directly, for example, by providing, instead ofaccelerometers 103, 104, a light source, such as a laser orlight-emitting diode (not shown), on the end of tip mass and sensorassembly 77 emitting light along the direction of the longitudinal axisof golf club shaft 110. A light sensitive detector array (also notshown) could be placed substantially perpendicular to the emitted lightbeam, which would trace the displacement of tip 112 on the detectorarray, recording the displacement directly. Regardless of how the dataare collected, they can be plotted as a function of time and used toderive displacement and frequency data that are then used, as describedabove, to mathematically determine the preferred angular orientation inwhich lies the planar oscillation plane. The direction of the planaroscillation plane closer to the estimated orientation determined by loadcell 91 would be considered the “hard” side of the principal planaroscillation plane or spine of golf club shaft 110, which preferablyshould be aligned perpendicular to, and facing, or in any otherpredetermined orientation with respect to, the club head face. However,the load cell test could be eliminated, insofar as aligning golf clubshaft 110 with the planar oscillation plane in a desired orientationwith respect to the club head face, whether the hard side of the planaroscillation plane faces toward or away from the face, is better thanhaving the planar oscillation plane at a random orientation relative tothe club head face, and also insofar as aligning any planar oscillationplane with respect to the club head face, even if it is not theprincipal planar oscillation plane, is better than a random orientation.It should be remembered, however, that if a random planar oscillationplane, rather than the principal planar oscillation plane, is found foreach golf club shaft in a set, then even if the planar oscillation planeso found for each shaft is oriented similarly relative to its respectiveclub head, the set cannot be assumed to be uniformly oriented.

[0068] Once the location of the spine has been determined, shaft 110preferably is marked to indicate the orientation of the spine, or atleast of the planar oscillation plane. Marking may be accomplished byapplying a pigment (e.g., paint or ink) to the surface of shaft 110. Forexample, an ink marker 130 having a marking tip 131 could be mounted ona frame 132 as shown in FIG. 13. After the preferred orientation hasbeen determined, shaft 110 can be rotated so that the preferredorientation is aligned with marking tip 131, which then applies a markto shaft 110. Alternatively, 130 could represent a paint reservoir,while 131 would represent a paintbrush. As a further alternative,marking of shaft 110 could be accomplished using a directed energy beamor a particle beam to etch a marking into the surface of shaft 110. Insuch an alternative, 130 could represent a high-energy laser, while 131would represent the laser beam, or 130 could represent an electron funwhile 131 would represent the electron beam. optionally, either shaft110 or the marking assembly could be moved parallel to the shaftlongitudinal axis so that the marking on the shaft is a line instead ofa dot, to increase its visibility.

[0069] The preferred method 140 according to the invention for locatingthe preferred orientation (i.e., either any planar oscillation plane orthe principal planar oscillation plane or “spine”), using apparatus 60,is diagramed in FIGS. 14-17. Method 140 preferably starts with load test141, described above, which uses load cell 91 to estimate theorientation of the principal planar oscillation plane and which at leastidentifies which of the two sides of the principal planar oscillationplane is the “hard” side of the planar oscillation plane. Load test 141could be omitted, but only if one is prepared to find any planaroscillation plane, rather than the principal planar oscillation plane inparticular. Where load test. 141 is performed, the result is used as astarting point for planar oscillation plane location step 143, below.Alternatively, load test 141 could be performed on a stand-alone basisto measure the symmetry of a shaft.

[0070] After load test 141 is performed, optional “logo up” test 142 isperformed. Conventional golf clubs are typically assembled with themanufacturer's logo, which is printed on the shaft, facing toward theclub head face, in what is referred to as a “logo up” configuration(some manufacturers align the logo 180° away from the club head face ina “logo down” configuration, or in other configurations). Because thelogo is printed at a random location on the shaft circumference, the“logo up” alignment is purely random. Logo up test 142 merely gathersdata regarding the oscillation of a golf club shaft in its factoryinstalled orientation.

[0071] As described above, planar oscillation plane location procedure143 is performed next. After procedure 143 has been performed, anoptional report printing step 144, in which some or all of variousparameters regarding the golf shaft whose preferred orientation has beenfound are printed. Finally, in an optional save step 145, various of thedata acquired during steps 141-144 are saved (e.g., in mass storage 64).

[0072] Load test 141 is shown in more detail in FIG. 15. At step 150, agolf club shaft 110, which may have been removed from a golf club, isplaced in chuck 76 at an arbitrary starting angle. Tip 112 of golf clubshaft 110 is deflected and restrained under shaft tip restraining arm 92so that the restoring force in the deflected shaft 110 is measured byload cell 91. The shaft can be deflected and secured manually, or thedeflection and securing can be accomplished automatically. Thus, an arm126 bearing a finger 127, driven by a motor 128, through suitablegearing or linkage 129 that provides the necessary horizontal andvertical components of motion, can be used to move tip 112 of golf clubshaft 110 from its neutral position 1200 to position 1201 under shafttip retention arm 92.

[0073] Once tip 112 is under shaft tip retention arm 92, then in step151 chuck 76 preferably is rotated about 2000 in one direction (whichmay be designated the negative rotation direction). Next, at step 152,chuck 76 is rotated at least 360° in the opposite direction (which maybe designated the positive rotation direction) while data is acquiredfrom load cell 91 and recorded as a function of angle. Preferably, instep 152, chuck 76 is rotated about 400° and 40° (preferably the firstand last 20°) is discarded. Alternatively, however, the reverse rotationof step 151 may be omitted, as long as data are recorded through atleast 360°, and if data are recorded through more than 360°, then anyamount of rotation greater than 360° may be used and any portion—all atthe beginning, all at the end, or any combination of beginning andend—may be discarded to provide 360° worth of data.

[0074] At step 153, the data gathered in step 152 are examined, and theangle A corresponding to the maximum load measured by load cell 91 isdetermined. If desired, the load as a function of angle may be graphedfor display. Next, at step 154, the start angle S, for use in planaroscillation plane location test 143, is set to A-90°. This takes intoaccount the change of orientation from vertical to horizontal as betweenthe load test 141 and the planar oscillation plane location test 143, asdescribed above.

[0075] After the conclusion of load test 141, “logo up” test 142, shownin detail in FIG. 16, may be conducted. The purpose of “logo up” test isprimarily to provide a “before” comparison to the “after” result to beobtained after performing planar oscillation plane location test 143.Therefore, as stated above, “logo up” test 142 is optional. Inparticular, while “logo up” test 142 may be used primarily as apromotional tool in an aftermarket situation—i.e., by a golf clubrefitter—to show the improvement obtained by realigning the shaft of agolf club in accordance with the invention, it probably would not beused by a golf club manufacturer who produces “spine-aligned” golfclubs, because there is no need to show comparative data.

[0076] “Logo up” test 142 begins at step 160 where golf club shaft 110,which, again, may have been removed from a golf club, is placed in chuck76. If it had previously been part of a completed golf club, shaft 110is placed in chuck 76 in the same orientation in which it was orientedin the golf club, as the club would have been positioned by a golferadjacent a ball before the start of the golfer's swing. In most cases,this would be with the manufacturer's logo facing up, but sometimes thelogo faces down or in a random direction. If test 142 is being performedon a golf club shaft that has never been part of a golf club, thenpreferably it is tested with its logo up. Tip mass and sensor assembly77 is then mounted on tip 112 of shaft 110.

[0077] Next, at step 161, an impulse is applied to tip mass and sensorassembly 77 in one of the ways described above andorthogonal—preferably, horizontal and vertical—acceleration data aregathered, preferably for about 4 seconds. These data preferably areintegrated at step 162 to yield orthogonal—preferably horizontal andvertical—displacement data as functions of time, which preferably aresaved at step 163 for later comparison with the results afterspine-alignment of shaft 110, and the data preferably also are graphedat step 163 for display to the owner of the golf club of which shaft 110is a part. The maximum out-of-plane displacement—i.e., preferably themaximum vertical displacement—preferably is also saved at step 163 fordisplay to the owner. Test 142 is now complete.

[0078] The system next proceeds to planar oscillation plane locationtest 143. As shown in FIG. 17, test 143 starts at step 170 where acounter J is initialized to zero. Next, at step 171, chuck 76, stillholding shaft 110, is rotated to the start angle S previously computed.If no start angle S has been computed, test 143 starts at an arbitraryangle.

[0079] At step 172, if tip mass and sensor assembly 77 has notpreviously been attached to tip 112 it is attached, and in any case animpulse is applied to tip mass and sensor assembly 77 in one of the waysdescribed above and orthogonal—preferably, horizontal andvertical—acceleration data are gathered, preferably for about 4 seconds.These data preferably are integrated at step 173 to yieldorthogonal—preferably horizontal and vertical—displacement data asfunctions of time. At step 174, the counter J is incremented by one. Attest 175, the system tests to see if J=1. If, as on this first pass,J=1, then the system skips directly to step 177.

[0080] At step-177, the system sets a variable YMAX(J) equal to themaximum out of plane deviation value from step 173. The-system thenproceeds to test 178 where it determines if J=1, meaning it is the firstpass through the loop. There preferably are always at least three passesthrough the loop. If at test 178 J=1, then at step 179 the angle S isincremented by 10°. At step 1700, in order to keep S between +180° and−180°, if S>180°, then S is set to S-360°. Next, at step 1701, thefrequencies of the horizontal and vertical oscillations are determined;this may be done from the displacement-vs.-time data from step 173.Frequency data are commonly used to measure the stiffness of golf clubshafts, and these data are useful for comparison.

[0081] After step 1701, the system loops back to step 172, and steps172-174 are carried out again. This time, at test 175 J≢1, and at step176 the data from step 173 are saved along with angle S, and the systemproceeds to step 177. Again at step 177 variable YMAX(J) is set equal tothe maximum out of plane deviation value from step 173. This time at

[0082] test 178 J≢1, and the system proceed to test 1702 to determine ifJ=2. On this second pass, J=2 and the system proceeds to test 1703 todetermine if YMAX(J)>YMAX(J−1). If not, that means in this iteration theout-of-plane excursions are smaller, meaning the angle S is closer tothe preferred orientation—i.e., to the planar oscillation plane—and atstep 1704 the variable SIGN is set to +1, the variable Y is set to thevalue of YMAX(J), and the variable AMP is set to 1.0, and the systemproceeds to step 1706. If at test 1703 YMAX(J)>YMAX(J−1), that means inthis iteration the out-of-plane excursions are larger, meaning the angleS is further from the planar oscillation plane, and at step 1705 thevariable SIGN is set to −1, the variable S(J) is set to the value ofS(J−1), the variable YMAX(J) is set to the value of the variableYMAX(J−1) and the variable Y is then set to the value of YMAX(J), andthe variable AMP is again set to 1.0, and the system proceeds to step1706. Note that in either step 1704 or step 1705, AMP can be set to ahigher value to cause the result to converge sooner, but with loweraccuracy, while setting AMP lower increases accuracy but increases thenumber of iterations before convergence. This is a trade-off betweenspeed and accuracy.

[0083] At step 1706 the system calculates the variablePOP=SIGN(45−(90/π)cos⁻¹ (Y/AMP)), and at step 1707 the value of S is setto S+POP. At step 1708, in order to keep S between +180° and −180°, ifS>180°, then S is set to S-360°. Similarly, at step 1709, in order tokeep S between +180° and −180°, if S<−180°, then S is set to S+360°. Thesystem then returns to step 1701 to calculate the frequencies, and onceagain loops back to step 172. This time, on the third pass, at test 178J≢1, and at test 1702 J≢2, and the system advances to test 1710 todetermine if YMAX(J)>YMAX(J−1). If it is, then the values areconverging, and the system proceeds to test 1711 to determine if theout-of-plane excursion on the last iteration (YMAX(J−1)) is less thanthe maximum out-of-plane excursion during the “logo up” test 142. If itis, then the current orientation is the preferred orientation, and atstep 1712 the variable POP, representing the preferred orientation, isset to the value of the variable S, representing the currentorientation. At step 1713, the shaft frequencies are again calculated asin step 1701, and test 143 ends at 1714.

[0084] If at test 1711, the out-of-plane excursion on the last iteration(YMAX(J−1)) is not less than the maximum out-of-plane excursion duringthe “logo up” test 142, then at step 1715, the variable POP,representing the preferred orientation, is set to the “logo up” angle.At step 1713, the shaft frequencies are again calculated as in step1701, and test 143 ends at 1714.

[0085] If at test 1710, YMAX(J)≯YMAX(J−1), then the values have notconverged, then at step 1715, Y is set to the value of YMAX(J). Thesystem then recalculates POP at step 1706 and from there goes throughthe loop at least one more time.

[0086] If optional “logo up” test 142 is not performed, then if test1710 indicates convergence, test 1711 is not performed and the systemproceeds directly from test 1710 to step 1712.

[0087] After completing planar oscillation plane location test 143, thesystem proceeds to report printing step 144 where the values of thefollowing data preferably are printed (and determined if necessary):load as a function of angle (as determined in load test 141); loadsymmetry index (LSI), which is a measure of the variability in stiffnessof the shaft (LSI=100(1−((P_(max)−P_(min))/P_(max))), where P_(max) andP_(min) are the maximum and minimum loads, respectively, measured instep 152); displacement plot at the “logo up” angle; displacement plotat the POP angle; displacement as a function of time at the “logo up”angle and the “hard” and “soft” POP angles (the latter two should beexactly 180° apart); the horizontal and vertical frequencies and themaximum out-of-plane excursions at the “logo up” and POP angles; and afrequency index equal to the ratio of the horizontal frequency at thePOP angle to the horizontal frequency at the “logo up” angle, which is acomparative measure, in the form of a percentage improvement, ofstiffness in the hit direction as between the original “logo up”configuration of the golf club and the spine-aligned configuration.

[0088] Next at step 145 the data are saved. In a full save, all data aresaved. There preferably is also a “quick save” in which all the dataprinted in step 144 are saved except for the complete load-vs.-angledata and the complete displacement data at the “logo up” and POP angles.Following saving step 145, process 140 ends at 146.

[0089] The process and apparatus according to the present invention canbe used as part of a larger process or apparatus for assembling golfclubs, to produce “spine-aligned” golf clubs. Thus, each golf club shaft110, having been marked with a reference mark at a predeterminedlocation relative to the location of the spine, preferred orientation,or planar oscillation plane (whether or not marked to indicate the“hard” side), can be passed to a golf club assembly station where themarking on the shaft is identified and used to assemble a golf club withthe spine or planar oscillation plane preferably substantiallyperpendicular to the golf club face. Depending on the relative speeds ofplanar oscillation plane locating apparatus 60 as compared to the golfclub assembly station, more or fewer planar oscillation plane locatingstations or assembly stations, as may be appropriate, can be provided.Thus, several planar oscillation plane location stations 60 may be usedto feed a single golf club assembly station. A hopper may be provided atthe golf club assembly station to act as a buffer in case the assemblystation slows down or stops, or is not ready to accept a new golf clubshaft 110 the moment the shaft arrives.

[0090] The golf club assembly station preferably is equipped with ascanner for identifying the mark made on golf club shaft 110 indicatingthe location of the planar oscillation plane. Once that mark has beenidentified, shaft 110 is rotated so that the mark is in a predeterminedorientation for the type of golf club head to be attached to shaft 110,and that golf club head is held in a predetermined orientation as shaft110 is assembled to the golf club head.

[0091] Alternatively, each golf club head could be provided with analignment marking to which the marking on golf club shaft 110 must bematched. A scanner scans for the alignment marks on both shaft 110 andthe golf club head and rotates shaft 110 until the two markings arealigned. This eliminates the need for the golf club head holdingmechanism to “know” a specific orientation in which to hold eachdifferent type of golf club head for alignment with the marked shaft.Instead, each golf club head can be held in the same orientation, and asshaft 110 is brought close for assembly, shaft 110 can be rotated untilthe marking on shaft 110 and the marking on the golf club head arealigned before shaft 110 is joined to the golf club head.

[0092] Apparatus 180 for assembling golf clubs in accordance with thepresent invention is shown in FIGS. 18 and 19. Apparatus 180 includes atleast one apparatus 60 (one shown), a conveyor 181 for removingcompleted shafts 110 from apparatus 60 and depositing them in a hopper182, a feed mechanism 183 for feeding each shaft 110 from hopper 182 toassembly station 184, and assembly station 184 itself.

[0093] At assembly station 184, feeder 183 including arms 185 connectedto a motor (not shown) delivers shaft 110 to chuck 190, similar to chuck76, which rotatably holds shaft 110 from its proximal end. Gripper 191holds a golf club head 192, which may or may not bear an alignmentmarking 193; if there is no alignment marking 193, golf club head 192 isheld by gripper 191 in a known position, which may differ for differenttypes of golf club heads. A scanner 194 scans shaft 110 for marking 195as chuck 190 rotates. When scanner 194 identifies marking 195, processor61 instructs chuck 190 to align marking 195 with alignment marking 193located by scanner 196, or with a predetermined orientation for golfclub head 192. Chuck 190 and gripper 191 are then moved together bymoving one or both thereof, and shaft 110 is joined to golf club head192 in an otherwise conventional way, using whatever adhesives,ferrules, etc. as may be necessary.

[0094] Thus it is seen that a method and apparatus for quickly andreliably determining the preferred angular orientation of a golf clubshaft, and for using the determination of the preferred angularorientation to automatically assemble golf clubs with each respectivegolf club shaft consistently aligned relative to the respective clubface, are provided. One skilled in the art will appreciate that thepresent invention can be practiced by other than the describedembodiments, which are presented for purposes of illustration and not oflimitation, and the present invention is limited only by the claimswhich follow.

What is claimed is:
 1. A method of determining a preferred angular orientation of a golf club shaft about a longitudinal axis thereof, said golf club shaft having a proximal end for gripping by a golfer and a distal end for attachment to a golf club head, said method comprising: immobilizing a first one of said proximal end and said distal end of said golf club shaft; initiating vibratory motion of a second one of said proximal end and said distal end of said golf club shaft in a direction other than parallel to said longitudinal axis; analyzing said vibratory motion; and calculating from said analyzed vibratory motion said preferred angular orientation.
 2. The method of claim 1 wherein: said first one of said proximal end and said distal end of said golf club shaft is said proximal end; and said second one of said proximal end and said distal end of said golf club shaft is said distal end.
 3. The method of claim 1 further comprising mounting a reaction mass on said distal end prior to said initiating.
 4. The method of claim 3 wherein said initiating comprises applying an impulse to said golf club shaft in a direction other than parallel to said longitudinal axis.
 5. The method of claim 4 wherein said applying an impulse comprises: displacing said distal end of said golf club shaft in a direction other than parallel to said longitudinal axis; and releasing said displaced distal end.
 6. The method of claim 1 wherein said initiating comprises applying an impulse to said golf club shaft in a direction other than parallel to said longitudinal axis.
 7. The method of claim 6 wherein said applying an impulse comprises: displacing said distal end of said golf club shaft in a direction other than parallel to said longitudinal axis; and releasing said displaced distal end.
 8. The method of claim 1 wherein said analyzing comprises measuring displacement over time of said distal end in at least two directions other than parallel to said longitudinal axis.
 9. The method of claim 8 wherein said two directions are perpendicular to each other and to said longitudinal axis.
 10. The method of claim 8 wherein said calculating comprises calculating based on said displacement measured over time.
 11. The method of claim 1 further comprising: deimmobilizing said proximal end; rotating said shaft through an angular displacement about said longitudinal axis; reimmobilizing said proximal end; and initiating subsequent vibratory motion of said distal end of said golf club shaft in a direction other than parallel to said longitudinal axis; wherein: said analyzing and said calculating are based also on said subsequent vibratory motion.
 12. The method of claim 11 further comprising iterating said deimmobilizing, said rotating, said reimmobilizing and said initiating, wherein said analyzing and said calculating are based also on each said subsequent vibratory motion, until said calculating converges on said preferred angular orientation.
 13. The method of claim 1 further comprising marking a visible indicium on said golf club shaft to indicate said preferred angular orientation.
 14. The method of claim 1 further comprising locating a hard side orientation by: displacing said distal end, in a direction other than parallel to said longitudinal axis, to a displaced condition; rotating said proximal end through at least about 360° of angular displacement while maintaining said distal end in said displaced condition; measuring force tending to restore said distal end from said displaced condition during said rotating, and associating measured force with angular displacement; and identifying as said hard side orientation an angular displacement associated with maximum measure force.
 15. The method of claim 14 wherein said locating is performed after said calculating.
 16. The method of claim 14 wherein said locating is performed prior to said immobilizing.
 17. The method of claim 16 wherein said direction of said initiating of said vibratory motion is said hard side orientation.
 18. A method of determining a preferred angular orientation of a golf club shaft about a longitudinal axis thereof, said golf club shaft having a proximal end for gripping by a golfer and a distal end for attachment to a golf club head, said method comprising locating a hard side orientation by: immobilizing a first one of said proximal end and said distal end of said golf club shaft; displacing a second one of said proximal end and said distal end, in a direction other than parallel to said longitudinal axis, to a displaced condition; rotating said immobilized end through at least about 360° of angular displacement while maintaining said displaced end in said displaced condition; measuring force tending to restore said displaced end from said displaced condition during said rotating, and associating measured force with angular displacement; and identifying as said hard side orientation an angular displacement associated with maximum measure force.
 19. The method of claim 18 further comprising: immobilizing a first one of said proximal end and said distal end of said golf club shaft; initiating vibratory motion of a second one of said proximal end and said distal end of said golf club shaft in a direction other than parallel to said longitudinal axis; analyzing said vibratory motion; and calculating from said analyzed vibratory motion said preferred angular orientation.
 20. Apparatus for determining a preferred angular orientation of a golf club shaft about a longitudinal axis thereof, said golf club shaft having a proximal end for gripping by a golfer and a distal end for attachment to a golf club head, said apparatus comprising: a clamp for immobilizing a first one of said proximal end and said distal end of said golf club shaft; a vibration generator for initiating vibratory motion of a second one of said proximal end and said distal end of said golf club shaft in a direction other than parallel to said longitudinal axis; at least one sensor for measuring said vibratory motion; and a processor for calculating from said measured vibratory motion said preferred angular orientation.
 21. The apparatus of claim 20 wherein: said clamp immobilizes said proximal end of said golf club shaft; and said vibration generator initiates vibratory motion of said distal end of said golf club shaft.
 22. The apparatus of claim 20 further comprising a reaction mass for mounting on said distal end prior to said initiating by said vibration generator.
 23. The apparatus of claim 22 wherein said at least one sensor is mounted on said reaction mass.
 24. The apparatus of claim 22 wherein said vibration generator applies an impulse to said golf club shaft in a direction other than parallel to said longitudinal axis.
 25. The apparatus of claim 24 wherein said vibration generator comprises: a restraint into which said distal end of said golf club shaft is displaced in a direction other than parallel to said longitudinal axis; and a release for freeing said displaced distal end from said restraint.
 26. The apparatus of claim 25 further comprising an actuator for displacing said distal end into said restraint.
 27. The apparatus of claim 20 wherein said vibration generator applies an impulse to said golf club shaft in a direction other than parallel to said longitudinal axis.
 28. The apparatus of claim 27 wherein said vibration generator comprises: a restraint into which said distal end of said golf club shaft is displaced in a direction other than parallel to said longitudinal axis; and a release for freeing said displaced distal end from said restraint.
 29. The apparatus of claim 28 further comprising an actuator for displacing said distal end into said restraint.
 30. The apparatus of claim 20 wherein said at least one sensor measures displacement over time of said distal end in at least two directions other than parallel to said longitudinal axis.
 31. The apparatus of claim 30 wherein said at least one sensor comprises two sensors, each measuring displacement over time in one of two directions other than parallel to said longitudinal axis.
 32. The apparatus of claim 31 wherein said two directions are perpendicular to each other and to said longitudinal axis.
 33. The apparatus of claim 30 wherein said processor calculates said preferred angular orientation based on said displacement measured over time.
 34. The apparatus of claim 20 wherein said clamp is rotatable, said apparatus further comprising: a restraint for maintaining said distal end in a displaced condition in a direction other than parallel to said longitudinal axis; a force transducer for measuring force tending to restore said distal end from said displaced condition, said clamp being rotated through at least about 360° of angular displacement during said measuring, while maintaining said distal end in said displaced condition; and memory in which measured force is associated with angular displacement; wherein: said processor identifies an angular displacement associated with maximum measured force as a hard side orientation.
 35. The apparatus of claim 34 further comprising a motor for rotating said clamp during said measuring.
 36. The apparatus of claim 34 further comprising an actuator for displacing said distal end into said displaced condition.
 37. The apparatus of claim 34 wherein said processor identifies said hard side orientation after calculating said preferred angular orientation.
 38. The apparatus of claim 34 wherein said processor identifies said hard side orientation prior to calculating said preferred angular orientation.
 39. The apparatus of claim 38 wherein said vibration generator initiates said vibratory motion in said hard side orientation.
 40. The apparatus of claim 20 further comprising a marker for making a visible indicium on said golf club shaft to indicate said preferred angular orientation.
 41. The apparatus of claim 40 wherein said marker applies pigment to said golf club shaft to make said visible indicium.
 42. The apparatus of claim 40 wherein said marker etches said visible indicium into said golf club shaft.
 43. The apparatus of claim 42 wherein said marker etches said visible indicium mechanically.
 44. The apparatus of claim 42 wherein said marker comprises a directed energy beam generator for making said visible indicium on said golf club shaft.
 45. The apparatus of claim 44 wherein said directed energy beam generator comprises a laser.
 46. A method of assembling a golf club, said golf club comprising a golf club shaft and a golf club head, wherein said golf club shaft has a preferred angular orientation relative to said golf club head, said method comprising: determining said preferred angular orientation of said golf club shaft about a longitudinal axis thereof, said golf club shaft having a proximal end for gripping by a golfer and a distal end for attachment to said golf club head, said determining comprising: immobilizing a first one of said proximal end and said distal end of said golf club shaft, initiating vibratory motion of a second one of said proximal end and said distal end of said golf club shaft in a direction other than parallel to said longitudinal axis, analyzing said vibratory motion, and calculating from said analyzed vibratory motion said preferred angular orientation; and attaching said golf club shaft to said golf club head with said preferred angular orientation in a predetermined relationship to said golf club head.
 47. The method of claim 46 wherein: said first one of said proximal end and said distal end of said golf club shaft is said proximal end; and said second one of said proximal end and said distal end of said golf club shaft is said distal end.
 48. The method of claim 46 further comprising mounting a reaction mass on said distal end prior to said initiating.
 49. The method of claim 48 wherein said initiating comprises applying an impulse to said golf club shaft in a direction other than parallel to said longitudinal axis.
 50. The method of claim 49 wherein said applying an impulse comprises: displacing said distal end of said golf club shaft in a direction other than parallel to said longitudinal axis; and releasing said displaced distal end.
 51. The method of claim 46 wherein said initiating comprises applying an impulse to said golf club shaft in a direction other than parallel to said longitudinal axis.
 52. The method of claim 51 wherein said applying an impulse comprises: displacing said distal end of said golf club shaft in a direction other than parallel to said longitudinal axis; and releasing said displaced distal end.
 53. The method of claim 46 wherein said analyzing comprises measuring displacement over time of said distal end in at least two directions other than parallel to said longitudinal axis.
 54. The method of claim 53 wherein said two directions are perpendicular to each other and to said longitudinal axis.
 55. The method of claim 53 wherein said calculating comprises calculating based on said displacement measured over time.
 56. The method of claim 46 further comprising: deimmobilizing said proximal end; rotating said shaft through an angular displacement about said longitudinal axis; reimmobilizing said proximal end; and initiating subsequent vibratory motion of said distal end of said golf club shaft in a direction other than parallel to said longitudinal axis; wherein: said analyzing and said calculating are based also on said subsequent vibratory motion.
 57. The method of claim 56 further comprising iterating said deimmobilizing, said rotating, said reimmobilizing and said initiating, wherein said analyzing and said calculating are based also on each said subsequent vibratory motion, until said calculating converges on said preferred angular orientation.
 58. The method of claim 46 further comprising marking a visible indicium on said golf club shaft to indicate said preferred angular orientation.
 59. The method of claim 46 further comprising locating a hard side orientation by: displacing said distal end, in a direction other than parallel to said longitudinal axis, to-a displaced condition; rotating said proximal end through at least about 360° of angular displacement while maintaining said distal end in said displaced condition; measuring force tending to restore said distal end from said displaced condition during said rotating, and associating measured force with angular displacement; and identifying as said hard side orientation an angular displacement associated with maximum measure force.
 60. The method of claim 59 wherein said locating is performed after said calculating.
 61. The method of claim 59 wherein said locating is performed prior to said immobilizing.
 62. The method of claim 61 wherein said direction of said initiating of said vibratory motion is said hard side orientation.
 63. The method of claim 46 wherein: said golf club head comprises a substantially planar face; and said predetermined relationship comprises a predetermined angular relationship between said preferred angular orientation of said golf club shaft and said substantially planar face.
 64. The method of claim 63 wherein said preferred angular orientation of said golf club shaft is substantially perpendicular to said substantially planar face.
 65. Apparatus for assembling a golf club, said golf club comprising a golf club shaft and a golf club head, wherein said golf club shaft has a preferred angular orientation relative to said golf club head, said apparatus comprising: an orientation detector for determining a preferred angular orientation of a golf club shaft about a longitudinal axis thereof, said golf club shaft having a proximal end for gripping by a golfer and a distal end for attachment to a golf club head, said orientation detector comprising: a clamp for immobilizing a first one of said proximal end and said distal end of said golf club shaft, a vibration generator for initiating vibratory motion of a second one of said proximal end and said distal end of said golf club shaft in a direction other than parallel to said longitudinal axis, at least one sensor for measuring said vibratory motion, and a processor for calculating from said measured vibratory motion said preferred angular orientation; and means for attaching said golf club shaft to said golf club head with said preferred angular orientation in a predetermined relationship to said golf club head.
 66. The apparatus of claim 65 wherein: said clamp immobilizes said proximal end of said golf club shaft; and said vibration generator initiates vibratory motion of said distal end of said golf club shaft.
 67. The apparatus of claim 65 further comprising a reaction mass for mounting on said distal end prior to said initiating by said vibration generator.
 68. The apparatus of claim 67 wherein said at least one sensor is mounted on said reaction mass.
 69. The apparatus of claim 67 wherein said vibration generator applies an impulse to said golf club shaft in a direction other than parallel to said longitudinal axis.
 70. The apparatus of claim 69 wherein said vibration generator comprises: a restraint into which said distal end of said golf club shaft is displaced in a direction other than parallel to said longitudinal axis; and a release for freeing said displaced distal end from said restraint.
 71. The apparatus of claim 70 further comprising an actuator for displacing said distal end into said restraint.
 72. The apparatus of claim 65 wherein said vibration generator applies an impulse to said golf club shaft in a direction other than parallel to said longitudinal axis.
 73. The apparatus of claim 72 wherein said vibration generator comprises: a restraint into which said distal end of said golf club shaft is displaced in a direction other than parallel to said longitudinal axis; and a release for freeing said displaced distal end from said restraint.
 74. The apparatus of claim 73 further comprising an actuator for displacing said distal end into said restraint.
 75. The apparatus of claim 65 wherein said at least one sensor measures displacement over time of said distal end in at least two directions other than parallel to said longitudinal axis.
 76. The apparatus of claim 75 wherein said at least one sensor comprises two sensors, each measuring displacement over time in one of two directions other than parallel to said longitudinal axis.
 77. The apparatus of claim 76 wherein said two directions are perpendicular to each other and to said longitudinal axis.
 78. The apparatus of claim 75 wherein said processor calculates said preferred angular orientation based on said displacement measured over time.
 79. The apparatus of claim 65 wherein said clamp is rotatable, said apparatus further comprising: a restraint for maintaining said distal end in a displaced condition in a direction other than parallel to said longitudinal axis; a force transducer for measuring force tending to restore said distal end from said displaced condition, said clamp being rotated through at least about 360° of angular displacement during said measuring, while maintaining said distal end in said displaced condition; and memory in which measured force is associated with angular displacement; wherein: said processor identifies an angular displacement associated with maximum measured force as a hard side orientation.
 80. The apparatus of claim 79 further comprising a motor for rotating said clamp during said measuring.
 81. The apparatus of claim 79 further comprising an actuator for displacing said distal end into said displaced condition.
 82. The apparatus of claim 79 wherein said processor identifies said hard side orientation after calculating said preferred angular orientation.
 83. The apparatus of claim 79 wherein said processor identifies said hard side orientation prior to calculating said preferred angular orientation.
 84. The apparatus of claim 83 wherein said vibration generator initiates said vibratory motion in said hard side orientation.
 85. The apparatus of claim 65 further comprising a marker for making a visible indicium on said golf club shaft to indicate said preferred angular orientation.
 86. The apparatus of claim 85 wherein said marker applies pigment to said golf club shaft to make said visible indicium.
 87. The apparatus of claim 85 wherein said marker etches said visible indicium into said golf club shaft.
 88. The apparatus of claim 87 wherein said marker etches said visible indicium mechanically.
 89. The apparatus of claim 87 wherein said marker comprises a directed energy beam generator for making said visible indicium on said golf club shaft.
 90. The apparatus of claim 89 wherein said directed energy beam generator comprises a laser.
 91. The apparatus of claim 85 wherein: said golf club head comprises a substantially planar face; said predetermined relationship comprises a predetermined angular relationship between said preferred angular orientation of said golf club shaft and said substantially planar face; and said means for attaching comprises: a detector for detecting said visible indicium, and an aligner for aligning said visible indicium in said predetermined angular relationship with said substantially planar face.
 92. The apparatus of claim 91 wherein said aligner aligns said visible indicium substantially perpendicular to said substantially planar face.
 93. The apparatus of claim 91 wherein: said golf club head is provided with a face alignment marking adjacent said substantially planar face; and said aligner aligned said visible indicium with said face alignment marking.
 94. Apparatus for determining a preferred angular orientation of a golf club shaft about a longitudinal axis thereof, said golf club shaft having a proximal end for gripping by a golfer and a distal end for attachment to a golf club head and being immobilized at a first one of said proximal end and said distal end for initiating vibratory motion of a second one of said proximal end and said distal end in a direction other than parallel to said longitudinal axis; said apparatus comprising: a reaction mass for mounting on said second one of said proximal end and said distal end prior to initiating said vibratory motion; at least one sensor mounted on said reaction mass for measuring said vibratory motion; and a processor for calculating from said measured vibratory motion said preferred angular orientation.
 95. The apparatus of claim 94 wherein said at least one sensor measures displacement over time of said distal end in at least two directions other than parallel to said longitudinal axis.
 96. The apparatus of claim 95 wherein said at least one sensor comprises two sensors, each measuring displacement over time in one of two directions other than parallel to said longitudinal axis.
 97. The apparatus of claim 95 wherein said two directions are perpendicular to each other and to said longitudinal axis.
 98. The apparatus of claim 95 wherein said processor calculates said preferred angular orientation based on said displacement measured over time.
 99. Apparatus for determining a preferred angular orientation of a golf club shaft about a longitudinal axis thereof, said golf club shaft having a proximal end for gripping by a golfer and a distal end for attachment to a golf club head and being immobilized at a first one of said proximal end and said distal end for initiating vibratory motion of a second one of said proximal end and said distal end in a direction other than parallel to said longitudinal axis, for computation of said preferred angular orientation based on said vibratory motion; said apparatus comprising: a reaction mass for mounting on said second one of said proximal end and said distal end prior to initiating said vibratory motion; and at least one sensor mounted on said reaction mass for measuring said vibratory motion.
 100. The apparatus of claim 99 wherein said at least one sensor measures displacement over time of said distal end in at least two directions other than parallel to said longitudinal axis.
 101. The apparatus of claim 100 wherein said at least one sensor comprises two sensors, each measuring displacement over time in one of two directions other than parallel to said longitudinal axis.
 102. The apparatus of claim 100 wherein said two directions are perpendicular to each other and to said longitudinal axis. 